I agree with Glacier and K9Soul. I would avoid trying to move him by his collar as it really is something many dogs don't love, and they can feel threatened by it. I hope you are able to use their advice to help. I'm sure he will come around.

You also have to realize he really doesn't know you yet, just like you really don't know him yet. You guys have to take more time and give him some slack to figure out how things work in your house. He will adjust, but he's new. He doesn't know your way of doing things yet, give him some time before you label him as stubborn, he may just be confused and probably scared honestly. I don't think he ran to your tub because he felt bad for mouthing you arm, he got scared with you grabbing him and mouthed your arm and when you let go he ran away to the tub because he was scared. It takes some practice but if you try to think like the dog, rather than thinking the dog has human emotions and thinks like you, it will be easier to understand him.